积分第一、二中值定理的中间点的渐近性质的一般性定理  

The General Asymptotic Property of the Intermediate Value of the First and Second Mean Value Theorem for the Integrals

作　　者：郑权[1] 

机构地区：[1]北方工业大学理学院,北京100041

出　　处：《数学的实践与认识》2005年第5期240-243,共4页Mathematics in Practice and Theory

摘　　要：把关于积分第一中值定理的中间点ξ的渐近性质的较多有关结果,归纳推广为一个弱条件下的一般性定理,并且在此弱条件下给出一种简洁的证明;而且,对于较少讨论的积分第二中值定理的中间点ξ的渐近性质,也得到相应的弱条件下的一般性定理,并且同样给出简洁证明.We absorb many results of the asymptotic property of the intermediate point of the first mean value theorem for the integrals into a general result, which has weak condition and is proved succinctly, and we also obtain a general result for the asymptotic property of the intermediate value of the second mean value theorem for the integrals, which is less discussed and is proved succinctly under the given weak condition too.

关 键 词：渐近性质 一般性 中间点 积分第一中值定理 积分第二中值定理 弱条件 证明 简洁 

分 类 号：O172.2[理学—数学]